It's likely that the holly is infested with scale insects. Scales suck the juices from the stems and undersides of the leaves of plants. Their excrement is a sticky, sugary substance that falls on th leaves and promotes the growth of bacteria, called sooty mold. This sooty mold is what turns the tops of the leaves black. Inspect your holly for the scale insects and hose them off, or squish them with your fingers. The sooty mold will weather off, or you can wash it off the surface of the leaves.